Problem: Multiply the following complex numbers, marked as blue dots on the graph: $[6(\cos(\frac{4}{3}\pi) + i \sin(\frac{4}{3}\pi))] \cdot [\cos(\frac{1}{3}\pi) + i \sin(\frac{1}{3}\pi)]$ (Your current answer will be plotted in orange.)
Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $6(\cos(\frac{4}{3}\pi) + i \sin(\frac{4}{3}\pi))$ ) has angle $\frac{4}{3}\pi$ and radius $6$ The second number ( $\cos(\frac{1}{3}\pi) + i \sin(\frac{1}{3}\pi)$ ) has angle $\frac{1}{3}\pi$ and radius $1$ The radius of the result will be $6 \cdot 1$ , which is $6$ The angle of the result is $\frac{4}{3}\pi + \frac{1}{3}\pi = \frac{5}{3}\pi$ The radius of the result is $6$ and the angle of the result is $\frac{5}{3}\pi$.